Co-induction in dynamical systems

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Journal Article
Ergodic Theory and Dynamical Systems, 2012, 32 (3), pp. 919 - 940
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If a countable amenable group G contains an infinite subgroup λ, one may define, from a measurable action of λ, the so-called co-induced measurable action of G. These actions were defined and studied by Dooley, Golodets, Rudolph and Sinelsh-chikov. In this paper, starting from a topological action of λ, we define the co-induced topological action of G. We establish a number of properties of this construction, notably, that the G-action has the topological entropy of the λ-action and has uniformly positive entropy (completely positive entropy, respectively) if and only if the λ-action has uniformly positive entropy (completely positive entropy, respectively). We also study the Pinsker algebra of the co-induced action. © 2011 Cambridge University Press.
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